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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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11
E F F, N C. HI V.
Concauo sermento hyperbolico inter duas asymproros parallelas intercepto, alud aequa
ausercur ab hyperbola, ad datam lineam parallelam asimptoto constitutu. pas. 587.
pr. 112.
SEquationes e comparationes varia seementorum duarum hyperbolarum coniusata
rum.
591. pr. 118. 2 sque 12.4.
Proprietates admiranda de superficiebus inter hyperbolam, asimptoton vnam e duas
parallelas alteri asymproto interiacentibus, totres sese continentibus, quoties certae ra
tiones linearum aut superficierum per parallelas illas abscissarum, continent ratio-
nes aliarum ejusmodi linearum aut superficierum:
594. pr. 123. 2 sque 129.
Linea parallela rniasymptotorum, inter alcerum asimproton es hyperbolam inter-
cepta, quae auferunt sermenta aequalia sunt omnes in continua analoeia. Duin e5
terminus procressionis harum proporcionalium assienatur.
597. pr. 130.
Terminus proeressionis exhibetur linearum quae ad se inuicem sint in duplicata ratione.
598. pr. 132.
Imo es minima exhibetur linea omnium quae in tali procressione dari possunt. 599.
Pr. 133.
Terminus proeressionis exhibetur linearum quae ad se invicem sint in triplicata ratione.
600. pr. 134.
Mira proprietas proeressionis linearum quae ad se inuicem sint in quadruplicata ratio-
ne siterminus huius proeressionis detur, ad inveniendas duas medias proportiona-
les
600. pr. 135. in Schol.
Yna e duabus mediis proportionalibus inter duas datas assenatur in hyperbola. 601.
pr. 136.
Imoc duae aspenantur conice.
602. pr. 137. 1300
Paralleloerammum assignatur aequale spatio comprehenso inter duas hyperbolas num-
quam concurrentes in infinitum, es sempermaxis ad se inuicem accedentes. 603.
Pr. 139.
R S QVIN F A
Eyperbon n pendie aparabola intersectam.
Ineae ni asumproto paratla expenduntur quae in duplicata, triplicata sint ra-
oe alat lost caermnararum. 604. pr. 140. 141. 142. pas. 608. pr. 149.
dementa per euosoat parallelas ablata à concaua hyperbola aequalia designantur.
605. pr. 143. 144. 145. pac. 607. pr. 147.
Item seemenca seementorum dupla, quadrupla. 606. pr. 146. pac. 607. pr. 148. Pae.
608. pr. 150. pas. 610. pr. 177.
Item mixtilinea mixtilineorum dupla.
G. Pr. 13l. 136.
Sparium interparabolam es hyperbolam, es quandam parallelam asymproto inceria
cens, cum alia quadam superficie comparatur.
610 pr. 153. 154.
Scementa per parallelas quasdam asymproro ablata ab hyperbola convexa comparantur
interse.
610. pr. 156.
Si linea eres sint parallelae asymptoto, quarum prima es proxima asimpeoto cui est
Pasatdelar auerase Pet Mtcectddten pat abola ed 1) Pet boled dstenartus quodralio
secundae
pas. 613 pr. 161. 162.
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